# Fits a mixture of Gaussian to CNV data

### Description

This function fits a mixture of Gaussians to Copy Number Variant data, both under the null hypothesis of no association and under the alternate hypothesis that the CNV frequencies differ between cases and controls.

### Usage

1 2 3 4 5 6 7 8 9 10 11 | ```
CNVtest.binary(signal, batch, sample = NULL, disease.status = NULL, ncomp,
n.H0 = 5, n.H1 = 0,
output = 'compact',
model.mean = "~ strata(batch, cn)",
model.var = "~ strata(batch, cn)",
model.disease ="~ cn",
association.test.strata = NULL,
beta.estimated = NULL,
start.mean = NULL,
start.var = NULL,
control = list(tol = 1e-05, max.iter = 3000,min.freq = 4))
``` |

### Arguments

`signal` |
The vector of intensity values, meant to be a proxy for the number of copies. |

`batch` |
Factor, that describes how the data points should be separated in batches, corresponding to different tehnologies to measure the number of DNA copies, or maybe different cohorts in a case control framework. |

`sample` |
Optional (but recommended). A character vector containing a name for each data point, typically the name of the individuals. |

`disease.status` |
In the case control situation a vector of 0 and 1 indicating which individuals are controls or cases. |

`ncomp` |
Number of components one wants to fit to the data. |

`n.H0` |
Number of times the EM should be used to maximize the likelihood under the null hypothesis of no association, each time with a different random starting point. The run that maximizes the likelihood is stored. |

`n.H1` |
Number of times the EM should be used to maximize the likelihood under the alternate hypothesis of association present, each time with a different random starting point. The run that maximizes the likelihood is stored. |

`output` |
The default value, “compact”, returns a data frame with one line per sample. Any other setting witll return a much bigger data frame with one line per individual and copy number. This long format is the one used by the underlying fitting algorithm and is only useful if one attempts to use CNVtools in a non standard manner. |

`model.mean` |
Formula that describes the linear model for the location of the mean signal intensity. The default is “~ strata(cn, batch)”, which means that the mean intensity can take any value for any combination of the variables “cn” (for copy number) and “batch”. More traditional model description such as ' ~ as.factor(cn)' for example are also possible, but are likely to be slower to fit and less numerically stable than the “strata” notation, which should be preferred. |

`model.var` |
A formula as above, but to model the variances. Whenever possible and to maximise speed and stability the model should be specified using the strata command, for example “strata(batch, cn)” (the default), meaning that variances are free to take any value for each combination of the variables “batch” and “copy number”. Alternatives such as “ ~ cn”, i.e. variance proportional to the number of copies are allowed but slower to fit, and less stable numerically. |

`model.disease` |
A formula that links the number of copies with the case/control status. The default is a logit linear trend model “~ cn”. Note that this formula will only matter under the alternate hypothesis and has no effect under the null (model descriptions using the “strata” command are not allowed for this model). |

`association.test.strata` |
Optional factor providing the strata when using a stratified test of association (typically, but not always, these are geographic regions of origins of the samples). |

`beta.estimated` |
Optional. It is used if one wants to fit the model for a particular value of the log odds parameter beta (essentially if one is interested in the profile likelihood). In this case the disease model should be set to ' ~ 1' and the model to 'H1'. It will then provide the best model assuming the value of beta (the log odds ratio parameter) provided by the user. |

`start.mean` |
Optional. A set of starting values for the means. Must be numeric and the size must match ncomp. This argument can also be a matrix if one wants to specify multiple starting points. When passing a matrix as argument, the number of columns should equal the number of components, and the number of rows must be greater than max(n.H0, n.H1). When in a row some numbers are missing, CNVtools will pick the starting points randomly (the default). |

`start.var` |
Optional. A set of starting values for the variances. Must be numeric and the size must match ncomp. Can also be a matrix (see start.mean for details). |

`control` |
A list of parameters that control the behavior of the fitting. min.freq is the minimum number of data points in a copy number class before the algorithm sets the frequency of this class to zero.In the presence of a very rare genotype group it might be useful to lower this threshold. Note, however, that estimating the variance if there are very few individuals in a class may not be possible, so setting options such as constant variances (i.e. model.var = ' ~1') might be sensible. |

### Value

`model.H0` |
The parameters for the best fit under H0. |

`posterior.H0` |
The output dataframe with the estimate posterior distribution under H0 as well as the most likely call. |

`status.H0` |
A character that describes the status of the fit under H0. The possible values are 'C' (converged), 'M' (maximum iterations reached), 'P' (posterior distribution problem). Fits that don't return 'C' should be excluded. |

`model.H1` |
The parameters for the best fit under H1. |

`posterior.H1` |
The output dataframe with the estimate posterior distribution under H1 |

`status.H1` |
A character that describes the status of the fit under H1. The possible values are 'C' (converged), 'M' (maximum iterations reached), 'P' (posterior distribution problem). Fits that don't return 'C' should be excluded. |

### Author(s)

Vincent Plagnol <vincent.plagnol@cimr.cam.ac.uk> and Chris Barnes <christopher.barnes@imperial.ac.uk>

### See Also

apply.pca apply.lda

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
#Load data for CNV for two control cohorts
data(A112)
raw.signal <- as.matrix(A112[, -c(1,2)])
dimnames(raw.signal)[[1]] <- A112$subject
#Extract CNV signal using principal components
pca.signal <- apply.pca(raw.signal)
#Extract batch, sample and trait information
batches <- factor(A112$cohort)
sample <- factor(A112$subject)
trait <- ifelse( A112$cohort == '58C', 0, 1)
#Fit the CNV with a three component model
fit.pca <- CNVtest.binary(signal = pca.signal, sample = sample, batch = batches,
disease.status = trait, ncomp = 3, n.H0=3, n.H1=3,
model.disease = "~ cn")
if(fit.pca[['status.H0']] == 'C' && fit.pca[['status.H1']] == 'C'){
#Calculate the likelihood ratio
LR <- -2*(fit.pca$model.H0$lnL - fit.pca$model.H1$lnL)
#Calculate the pvalue. Has 1 dof since we fit a trend model
pvalue <- 1 - pchisq(LR,1)
}
``` |